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Infinity Is Big As Universe?

Today, I would like to discuss on how big infinity is. Have you ever think about this? Since I was 7 years old, I always asked my teachers what is the last number?

“It’s more than what you think”

I don’t satisfied with the answer. So, when I went to the secondary school, I asked my teacher the same question.

“The biggest number is Infinity”

But, I came out with another question! What is infinity? I want a value like ∞ = 99987654321082. I keep asking myself how big a number can be? *I feel like eating something sweet right now because I’M HAPPY*

INFINITY HAS NO END

Infinity is the idea of something that has no end.

In our world we don’t have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity.

So don’t think like that (it just hurts your brain!). Just think “endless”, or “boundless”.

If there is no reason something should stop, then it is infinite.

INFINITY DOES NOT GROW

Infinity is not “getting larger”, it is already fully formed.

Sometimes people (including me) say it “goes on and on” which sounds like it is growing somehow. But infinity does not do anything, it just is.

INFINITY IS NOT A REAL NUMBER

Infinity is not a real number, it is an idea. An idea of something without an end.

Infinity cannot be measured.

Even these faraway galaxies can’t compete with infinity.

INFINITY IS INFINITE

All of these numbers are “finite”, we could eventually “get there”.

But none of these numbers are even close to infinity. Because they are finite, and infinity is … notfinite!

USING INFINITY

We can sometimes use infinity like it is a number, but infinity does not behave like a real number. To help you understand, think “endless” whenever you see the infinity symbol “∞”:

For example: ∞ + 1 = ∞

Which says that infinity plus one is still equal to infinity. When something is already endless, we can add 1 and it is still endless. The most important thing about infinity is that:

–∞ < x < ∞

Where x is a real number

Which is mathematical shorthand for “negative infinity is less than any real number,
and infinity is greater than any real number”

Here are some more properties:

Special Properties of Infinity

∞ + ∞ = ∞

-∞ + -∞ = -∞

∞ × ∞ = ∞

-∞ × -∞ = ∞

-∞ × ∞ = -∞

x + ∞ = ∞

x + (-∞) = -∞

x – ∞ = -∞

x – (-∞) = ∞

For x>0 :

x × ∞ = ∞

x × (-∞) = -∞

For x<0 :

x × ∞ = -∞

x × (-∞) = ∞

Undefined Operations

All of these are “undefined”:

0 × ∞

0 × -∞

∞ + -∞

∞ – ∞

∞ / ∞

∞0

1∞

Example: Isn’t ∞ / ∞ equal to 1?

No, because we really don’t know how big infinity is, so we can’t say that two infinities are the same. For example ∞ + ∞ = ∞, so

∞∞ = ∞ + ∞∞

which
means that:

11 = 21

?

And that doesn’t make sense!

I could have also made 1=3 and so on … so we say that ∞ / ∞ is undefined.